Image sampling. Transition from continuous signals and transformations to discrete discrete image

Images consisting of discrete elements each of which can only receive a finite number of distinguishable values \u200b\u200bthat change in the final time are called discrete. It should be emphasized that the elements of the discrete image, generally speaking, may have an unequal area and each of them may have an unequal number of distinguishable gradations.

As shown in the first chapter, the retina transmits discrete images to the highest departments of the visual analyzer.

Their apparent continuity is only one of the illusions of view. This "quantization" of initially continuous images is not determined by the constraints that are associated with the resolution of the optical system of the eye and not even the morphological structural elements of the visual system, but the functional organization of nervous networks.

The image is divided into discrete elements by recipe fields that combine one or another number of photoreceptors. Recipe fields produce primary selection of the useful light signal by spatial and temporal summation.

The central part of the retina (Fovaa) is occupied only by the columns, on the periphery outside the Fovaa, there are both columns and wands. Under nightlife conditions, the colummer fields in the central part of the retina have approximately the same value (about 5 "in the angular measure). The number of such fields in Fovaa, the angular dimensions of which are about 90", about 200. The main role in nightpoints is played by sticky fields. The rest of the retina surface. They have an angular size of about 1 ° all over the entire surface of the retina. The number of such fields in the retina is about 3 thousand. Not only detection, but also the viewing of weakly illuminated objects under these conditions is performed by peripheral sections of the retina.

With an increase in the illumination, the main role is started to play the other cumulative cells - columine receptive fields. In Fovaa, an increase in illumination causes a gradual decrease in the efficient value of the field, while the brightness of the order of 100 ASB does not reduce to one columination. On the periphery with increasing illumination gradually turn off (brake) sticky fields and the columns come into effect. Colummer fields on the periphery are like a fowel with the ability to decrease depending on the light energy falling on them. The greatest amount of colums that can have columine receptive fields with increasing illumination, grows from the center to the edges of the retina and at the angular distance of 50-60 ° from the center reaches approximately 90.

You can calculate that in the conditions of good day lighting The number of recipe fields reaches about 800 thousand. This value approximately corresponds to the number of fibers in the audience nerve of the person. The distinction (permission) of objects in daylight is carried out mainly by Fovtea, where the receptive field can be reduced to one columination, and the columns themselves are located most tight.

If the number of rigid cumulative cells can be determined in a satisfactory approximation, then there is no sufficient data to determine the number of possible conditions of recipe fields. Only some-estimates can be made based on the study of differential rapids of recipe fields. The threshold contrast in the foxal receptive fields in a certain working range of illumination has order 1. At the same time, the number of distinguishable gradations is small. In the entire range of perestroika, the colummer fowel recipe field differs 8-9 gradations.

The period of accumulation in the recipe field is the so-called critical duration - is determined by an average of about 0.1 seconds., But at high levels of lighting, it can seem to significantly decrease.

In fact, the model describing the discrete structure of the transmitted images should be even more complicated. It would be necessary to take into account the relationship between the size of the recipe field, thresholds and critical duration, as well as the statistical nature of visual thresholds. But so far there is no need for this. It is enough to present as a model of the image the set of the same in the area of \u200b\u200bthe elements, the angular sizes of which are smaller than the angular dimensions of the smallest-resolved part of the part, the number of distinguishable states of which are greater than the maximum number of distinguished gradations of brightness, and the time of the discrete change of which is smaller than the fracture period during critical Freight frequency flashes.

If you replace images of real continuous objects external world Such discrete images, the eye will not notice the substitution. * Consequently, discrete images of this kind contain at least no less information than the visual system perceives. **

* Color and volumetric images can also be replaced by a discrete model.
** The problem of replacing continuous images is discrete is important for film and television techniques. Temporary quantization underlies this technique. In the pulse-code television systems, the image, in addition, is divided into discrete elements and quantum on brightness.

Consider a continuous image - the function of two spatial variables x. 1 I. x. 2 f.(x. 1 , x. 2) on a limited rectangular region (Figure 3.1).

Figure 3.1 - Transition from continuous image to discrete

We introduce the concept of a sampling step Δ 1 by spatial variable x. 1 and Δ 2 by variable x. 2. For example, it can be represented that at points removed from each other at a distance δ 1 along the axis x. 1 Located point video sensors. If these video sensors are installed throughout the rectangular area, the image will be given on a two-dimensional grid

To reduce the record we denote

Function f.(n. 1 , n. 2) is a function of two discrete variables and is called a two-dimensional sequence. That is, the sampling of the image along the spatial variables translates it into the table of selective values. The dimension of the table (the number of rows and columns) is determined by the geometric sizes of the source rectangular region and the choice of sampling step by the formula

Where the square brackets [...] denote the integer part of the number.

If the continuous image definition area is a square L. 1 = L. 2 = L,and sampling step is chosen the same on the axes x. 1 I. x. 2 (δ 1 \u003d δ 2 \u003d δ)

and the dimension of the table is N. 2 .

The element of the table obtained by sampling the image is called " pixel "or " countdown". Consider pixel f.(n. 1 , n. 2). This number takes continuous values. Computer memory is able to store only discrete numbers. Therefore, to write in memory. Continuous value f.must be subjected to analog-to-digital transformation in step D f. (see Figure 3.2).

Figure 3.2 - Quantization of continuous magnitude

The operation of analog-to-digital transformation (discretization of the continuous value in terms of level) is often called quantization. The number of quantization levels, provided that the values \u200b\u200bof the brightness function lie in the range _____ _ _______, equal

In practical image processing tasks Q.varies widely from Q.\u003d 2 ("binary" or "black and white" images) to Q.\u003d 210 or more (almost continuous brightness values). Most often choose Q.\u003d 28, while the image pixel is encoded by one byte of digital data. Of all the above, we conclude that the pixels stored in the memory of the computer are the result of the discretization of the original continuous image of the arguments (coordinates?) And levels. (Where and how much, and everything is discrete) it is clear that the sampling steps δ 1 , Δ 2 should be selected small enough to ensure that the sampling error is insignificant, and the digital representation retained the basic information about the image.

It should be remembered that the smaller the sampling step and quantization, the greater the amount of image data should be recorded in the computer's memory. Consider as an illustration of this statement an image on a slide size of 50 × 50 mm, which is introduced into memory using a digital optical density meter (microstensitometer). If when you enter a linear resolution of a microstensitometer (sampling step on spatial variables) is 100 microns, then a two-dimensional array of pixels of dimension is recorded in memory N. 2 \u003d 500 × 500 \u003d 25 ∙ 10 4. If the step is reduced to 25 microns, then the size of the array will increase by 16 times and constitute N. 2 \u003d 2000 × 2000 \u003d 4 ∙ 10 6. Using quantization of 256 levels, that is, encoding the byte found by the pixel, we obtain that in the first case, a volume of 0.25 megabytes of memory is required for recording, and in the second case 4 megabytes.

Analog and discrete ways of presenting images and sound

The person is able to perceive and store information in the form of images (visual, sound, tactile, taste and olfactory). Visual images can be saved in the form of images (drawings, photos and so on), and sound - fixed on plates, magnetic tapes, laser disks and so on.

Information, including graphic and sound, can be represented in analog or discrete form. With analog representation, the physical value takes an infinite set of values, and its values \u200b\u200bchange continuously. With a discrete view, the physical value takes a finite set of values, and its value changes jumps like.

We give an example analog and discrete presentation information. The position of the body on the inclined plane and on the staircase is set to the values \u200b\u200bof the coordinates X and Y. When the body moves along the inclined plane, its coordinate can take an infinite set of continuously changing values \u200b\u200bfrom a certain range, and when the stairs moves, only a certain set of values, and changing jump-like (rice . 1.6).

An example of analog representation graphic information It can serve, for example, a pictorial canvas, the color of which changes continuously, and the discrete - an image printed with inkjet printer and consisting of separate points of different colors. An example of analog storage sound information is an vinyl record (The audio track changes its form continuously), and the discrete - audio component (which contains areas with different reflectivity).

Convert graphic and sound information from analog form to discrete is made by discretization, that is, partitioning continuous graphic image and continuous (analog) sound signal on the separate elements. In the sampling process, coding is made, that is, the assignment to each element of a specific value in the form of code.

Sampling - This is a conversion of continuous images and sound in a set of discrete values \u200b\u200bin the form of codes.

Questions for reflection

1. Give examples of analog and discrete ways to represent graphic and sound information.

2. What is the essence of the discretization process?

In the information processing system, the signals come, as a rule, in continuous form. For computer processing continuous signals It is necessary, first of all, to convert them into digital. For this, sampling and quantization operations are performed.

Discretization of images

Sampling - This is a conversion of a continuous signal into a sequence of numbers (samples), that is, the presentation of this signal according to any finite-dimensional basis. This view is in the design of the signal to this basis.

The most convenient to organize processing and the natural way of sampling is the representation of signals in the form of sampling their values \u200b\u200b(samples) in separate, regularly located points. This method is called rastrier, and the sequence of nodes in which the counts are taken - raster. The interval through which the continuous signal values \u200b\u200bare called sampling step. The reverse step is called sampling frequency,

A significant question arising during sampling: What frequency to take the signal counts in order to be the possibility of its reverse recovery on these references? Obviously, if you take the counts too rarely, then they will not contain information about the rapidly changing signal. The speed of the signal change is characterized by the upper frequency of its spectrum. Thus, the minimum allowable sampling interval width is associated with the highest frequency of the signal spectrum (inversely proportional to it).

For the case of uniform sampling is valid theorem Kotelnikov, published in 1933 in the work "about bandwidth Ether and wire in telecommunication. " It reads: if a continuous signal has a spectrum bounded by the frequency, then it can be completely and uniquely restored by its discrete references taken with a period, i.e. With frequency.

Signal recovery is carried out using a function. . Kotelnikov It was proved that a continuous signal that satisfies the above criteria can be represented as a series:

.

This theorem is also also called the counting theorem. The function is called back countdown or kotelnikovAlthough the interpolation series of this species studied still Whitaker in 1915. The reading function has an infinite length of time and reaches the greatest value equal to one, at a point, with respect to which it is symmetric.

Each of these functions can be viewed as a response of the perfect filter low frequency (FNH) on delta-impulse, which came at the time of time. Thus, to restore the continuous signal from its discrete samples, they must be skipped through the corresponding FNF. It should be noted that such a filter is anegous and physically unrealized.

The reduced ratio means the ability to accurately restore signals with a limited spectrum on the sequence of their samples. Limited spectrum signals - These are signals, the Fourier spectrum is different from zero only within a limited area of \u200b\u200bthe definition area. Optical signals can be attributed to them, because The Fourier spectrum of images obtained in optical systems is limited due to the limited size of their elements. The frequency is called the frequency of Nyquista. This limit frequency above which there should be no spectral components in the input signal.

Quantization of images

With digital image processing, the continuous dynamic range of brightness values \u200b\u200bis divided into a number of discrete levels. This procedure is called quantization. Its essence is to convert a continuous variable to a discrete variable that takes the final set of values. These values \u200b\u200bare called quantization levels. In general, the transformation is expressed by a stepped function (Fig. 1). If the image countdown intensity belongs to the interval (i.e., when ), the initial countdown is replaced by the quantization level, where – quantization thresholds. It assumes that the dynamic range of brightness values \u200b\u200bis limited and is equal.

Fig. 1. Function describing quantization

The main task is to determine the values \u200b\u200bof thresholds and quantization levels. The simplest way solutions to this task is to break dynamic range At the same intervals. However, such a decision is not the best. If the intensity values \u200b\u200bof most image samples are grouped, for example, in the "dark" region and the number of levels is limited, then it is advisable to quantize unevenly. In the "dark" region follows quantum more often, and in "light" less often. This will reduce quantization error.

In digital image processing systems, they seek to reduce the number of levels and quantization thresholds, since the amount of information required for encoding the image depends on their quantity. However, with a relatively small number of levels on a quantized image, false contours may appear. They arise due to the jump-like change in the brightness of the trocked image and are especially noticeable on the gentle plots of its change. False contours significantly worsen the visual image quality, since the sight of a person is especially sensitive to contours. With uniform quantization of typical images, at least 64 levels are required.

To tell and show on the example of Pascal: 1) What is Absolute and what is needed for? 2) What is ASM and for what is needed? 3) what is

constructor and Destructor and for what is needed?

4) What is IMPLEMENTATION and what is needed?

5) Call Pascal Modules (in the Usses string, for example CRT) and what capabilities do this module gives?

6) What kind of variable type: Signable (Pointer)

7) And last time: what does the @, #, $, ^ symbol mean

1. What is the object? 2 What is the system? 3. What is the common name of the object? Give example.4. What is the unit name of the object? Bring example.5.

Give an example of a natural system.6. Give an example of a technical system. 7 Give an example of a mixed system.8. Give an example of an intangible system.9. What is classification? 10. What is the object class?

1. 23 Question - List the operation modes of the DBMS ACCESS:

Creating a table in constructor mode;
- Creating a table with the help of a wizard;
- Creating a table by entering data.

2. What is a vector format?

3. Is it possible to attribute the following to service programs:
a) disk service programs (copying, treatment, formatting, etc.)
b) compression of files on disks (archivers)
c) combat computers and much more.
i myself think what's the answer here b - right or not?

4. What belongs to the properties of the algorithm (a. Discreteness, b. Performance in. Massiness, definition, feasibility and understandable) - Here I think that all options are correct. Right or not?

Test 7 lecture questions with the choice of response

13. Processor clock frequency is:

A. The number of binary operations performed by the processor per unit of time

B. Number of pulses generated in one second, synchronizing computer nodes

C. The number of possible processor appeals to random access memory per unit of time

D. Information exchange rate between the processor and I / O devices

14. For the minimum necessary set of devices designed to work for the computer:

A. Printer system unit, keyboard

B. Processor, RAM, Monitor, Keyboard

C. Processor, Stremmer, Winchester

D. Monitor, System Block, Keyboard

15. What is a microprocessor?

A. integral microcircuitwhich performs the commands entering it and manages

Working computer

B. Device for storing those data that is often used in

C. Device for the output of text or graphic information

D. Device for the output of alphanumeric data

16. Interaction of the user with the software medium is carried out using:

A. Operating system

B. File System

C. Apps

D. File Manager

17. Emergency management software The user can exercise with

Help:

A. Operating system

B. Graphic interface

C. User Interface

D. File Manager

18. Methods for storing data on physical media determines:

A. Operating system

B. Applied Software

C. File system

D. File Manager

19. The graphic environment on which objects and controls are displayed. windows systems,

Created for user convenience:

A. Hardware interface

B. User interface

C. Desk

D. Software interface

20. The speed of the computer depends on:

A. Processor clock frequency

B. Availability or absence of a connected printer

C. Operating system interface organizations

D. Volume of an external storage device